The reason you should not be allowed to have hair dye in school is not whether it is fair or not but wether it causes harm to the other students ability to learn in the classroom enviroment.

[1]It has been known that most students can be distracted by bright colours, lights, and noises so if a student were to wear a bright pink dye in their classroom then that can be harmful to the other students learning capabilities until the dye(s) can be washed, decays, or is removed with greater time.

Then again, what you wear in your school is not dictated on what is right or wrong but rather its dresscode. If the school specificly tells you cannot wear a specific item, then you cannot wear that item, and this does include hair dye. "However, the ACLU believes that to punish you for your hairstyle or body piercings, your school should have to show that they were disruptive or caused a valid health or safety risk." Which it is very clear that you cannot be punnished for long hair, but, hair dye is a disruptive 'object' in the learning inviroment.[1]

Another fact is that hair dye can be destramental to the students health; cancer. [3]

Temporary dyes: These dyes cover the surface of the hair but don’t penetrate into the hair shaft. They generally last for 1 to 2 washings.

Semi-permanent dyes: These dyes do penetrate into the hair shaft. They typically last for 5 to 10 washings.

Permanent (oxidative) hair dyes: These dyes cause lasting chemical changes in the hair shaft. They are the most popular types of hair dyes, because the color changes last until the hair is replaced by new growth. These dyes are sometimes referred to as coal-tar dyes because of some of the ingredients in them. They contain colorless substances such as aromatic amines and phenols. In the presence of hydrogen peroxide, these substances go through chemical reactions to become dyes. Darker hair dyes tend to use more of these coloring agents.

Permanent hair dyes are the most common dyes that cause cancer do to the increase in carcinogens. [2]